Most materials expand when they are heated and contract when they are cooled. Although it is rare, some materials expand when they are cooled, and therefore have a negative thermal expansion upon heating instead of a positive thermal expansion. Materials that exhibit a very low thermal expansion are useful primarily because of their resistance to damage from thermal shock on rapid heating or rapid cooling. However, either a/tow positive thermal expansion or the NTE effect for a particular compound may be sufficient to compensate for the positive thermal expansion coefficient of usual materials. For instance, combining low positive thermal expansion materials or NTE materials with other materials, such as ceramics and epoxies, would provide a composition that shows exceptionally low thermal expansion or contraction. Ceramics are stressed by abrupt expansion or contraction during temperature cycling, which may result in mechanical failure. "Thermal Expansion of ZrP.sub.2 O.sub.7 and Related Solid Solutions," J. Materials Science, 22:3762-3764 (1987). Thus, adding a sufficient amount of an NTE material to a ceramic to form a ceramic-NTE composition would alleviate some of the stress induced by temperature changes.
Materials that exhibit negative thermal expansion or a small positive thermal expansion are known. Unfortunately, known compounds exhibit NTE only over certain temperature ranges, particularly temperatures above about 150.degree. C., and therefore are not suitable for most applications. Moreover, most known NTE materials have highly anisotropic thermal expansion. Anisotropic thermal expansion means that a compound expands in certain dimensions while contracting in at least one dimension. The magnitude of the contraction (negative expansion) in a first direction may be offset by expansion in a second direction. Hence, even though the sum of the expansion in all dimensions (the bulk expansion) may be negative, the magnitude of the negative expansion is reduced. It therefore would be preferable if the NTE was isotropic, i.e., if thermal expansion was substantially negative in each dimension. Isotropic NTE behavior also is important because anisotropic behavior may cause undesirable strain to occur in a material as it undergoes a change in temperature.
Keatite is a first example of a material that exhibits anisotropic negative linear expansion. Keatite is a rare and poorly defined form of SiO.sub.2. The result of both thermal expansion and contraction in different directions (anisotropic expansion) for Keatite is a net negative thermal volume expansion. A second example of an anisotropic NTE material is .beta.-eucryptite, which exhibits a very small volume thermal expansion. Apparently, .beta.-eucryptite expands in one direction of the material's unit cell (a unit cell is defined as the simplest, three dimensional polyhedron that by indefinite repetition makes up the lattice of a crystal and embodies all the characteristics of its structure), whereas the unit cell contracts in a second direction. "Thermal Contraction of .beta.-Eucryptite (Li.sub.2 O.Al.sub.2 O.sub.3.2SiO.sub.2) by X-ray and Dilatometer Methods," J. Am. Ceram. Soc., 42:175-177 (1959). The overall thermal expansion of .beta.-eucryptite is reported to be either slightly positive or slightly negative.
(ZrO).sub.2 P.sub.2 O.sub.7 (zirconyl phosphate) and ZrV.sub.2 O.sub.7 (zirconium pyrovanadate) also are known compounds that exhibit NTE. (ZrO).sub.2 P.sub.2 O.sub.7 is a largely anisotropic material that expands in two directions while actually contracting in only one direction. More specifically, the a and c axes of the unit cell for (ZrO).sub.2 P.sub.2 O.sub.7 expand continuously with increasing temperature, while the b axis contracts. "Low-Thermal-Expansion Polycrystalline Zirconyl Phosphate Ceramic," J. Am. Ceram. Soc., 68:273-278 (1985). The net effect is a small volume contraction over a limited temperature range, although ceramic materials made from (ZrO).sub.2 P.sub.2 O.sub.7 actually are reported to have a small positive thermal expansion (actual value=+2.0.times.10.sup.-6 /.degree.C.). Zirconium pyrovanadate also has been shown to exhibit negative thermal expansion. However, NTE for this compound occurs only above a temperature of about 150.degree. C. "Properties of Hot-Pressed Zirconium Pyrovanadate Ceramics," J. Electrochem. Soc., 130:1905-1910 (1983).
In addition to the NTE materials described above, compounds of the type A.sup.4+ P.sub.2 O.sub.7 exist where A.sup.4+ may be Th, U, Ce, Hf, Zr, Ti, Mo, W, Pb, Sn, Ge or Si. The basic structure for such compounds may be thought of as related to the NaCl structure. NaCl molecules are arranged in cubes wherein the Na.sup.+ and the Cl.sup.- ions are located at alternating corners of the cube. With A.sup.4+ P.sub.2 O.sub.7 compounds, A.sup.4+ has replaced Na+, and the (P.sub.2 O.sub.7).sup.4- group has replaced Cl.sup.-. Some compounds of the A.sup.4+ P.sub.2 O.sub.7 type show low thermal expansion behavior when they are at temperatures well above normal ambient temperature, and some even show NTE behavior at temperatures well above room temperature. For example, ThP.sub.2 O.sub.7 shows NTE behavior above about 300.degree. C. However, there have been no reports of NTE behavior in A.sup.4+ P.sub.2 O.sub.7 materials at or below about 100.degree. C.
Hence, a need exists for new materials that exhibit isotropic NTE, particularly where the temperature at which NTE behavior begins (NTE onset temperature) is within the range of about 100.degree. C. Furthermore, a need exists for a homologous family of NTE materials in which the NTE onset temperature for each compound is different from other compounds within the family, or wherein the NTE onset temperature can be determined by varying the atomic ratios of the constituent elements. Such a family of compounds would provide a means for selecting a particular compound, having a particular NTE magnitude and onset temperature, to be used for a particular application.